Northern Virginia students passed state mathematics tests this year at a far lower rate than in previous years, a drop echoed statewide and which officials attribute to tougher exams.

State officials reported Tuesday that the pass rates in math for most students in grades three through eight and for those taking algebra and geometry in various secondary grades were at least 10 percentage points lower for the school year that recently ended.

In some Northern Virginia school systems, the pass rates for certain grades plummeted by more than 40 percentage points. In Alexandria public schools, for instance, 22 percent of eighth-graders passed state math exams, compared with 62 percent in the 2010-11 year.

“We are all disappointed the results in math are not higher than they are,” Patricia I. Wright, Virginia’s superintendent of public instruction, said Tuesday. She noted that there were similarly low pass rates in 2006, when Virginia began Standards of Learning tests for sixth- and seventh-graders.

Statewide, only sixth-grade scores held steady: a 74 percent pass rate in the 2011-12 school year, compared with 73 percent in the 2010-11 school year. (In Northern Virginia, there was a notable increase in test scores among most sixth-graders. Arlington County’s sixth-graders, for example, passed at a rate of 81 percent, compared with 65 percent last year.)

In English, the Virginia Department of Education reported that pass rates for reading and writing across grades three through eight remained mostly unchanged. Reviews of scores in Fairfax County and elsewhere in Northern Virginia showed similar trends.

Virginia Board of Education President David Foster said Tuesday that the lower math pass rates were expected. The new Standards of Learning tests require students to use multi-step problem-solving techniques and cover material that used to be taught at a higher level. The more rigorous exams, phased in starting in 2011, are designed to better prepare students for college and careers after high school.

In addition, the lower pass rates reflect a 2009 decision by the Virginia Board of Education to raise math standards.

Gov. Robert F. McDonnell (R) said in a statement that “these new challenging standards” are meant to ensure that “Virginia students are ready to excel in our globally competitive economy.”

The most significant decreases in math pass rates were among students in grades three, seven and eight, largely because of revamped tests that included more-advanced concepts.

Statewide, 60 percent of eighth-graders passed the tests. Last year, 82 percent passed. Among seventh-graders, 58 percent passed, compared with 77 percent the year before. For third-graders, the statewide passing rates fell to 64 percent from 91 percent in 2010.

The same trends were seen in Northern Virginia public schools. The pass rate for eighth-graders in Loudoun County fell from 80 percent to 33 percent. For eighth-graders in Manassas City schools, the pass rate decreased from 69 percent to 12 percent.

While the pass rates in all grades dropped, Fairfax schools outperformed the statewide math average. More than 75 percent of all seventh- and eighth-graders in Fairfax passed the new math tests.

Wright said that schools with significant drops in math pass rates will be placed on a watch list. Those that continue to have pass rates below 70 percent, she said, could face accreditation issues.

Past teaching practices involving intense preparation for the Standards of Learning tests, she said, will not be sustainable.

“These standards are attainable,” Wright said. “Just ‘drill and kill’ is not the answer for these tests.”